Performance analysis of OMP algorithm in recovering magnitude decaying sparse signals in compressive sensing

The sparse signal recovery has been the subject of extensive research in several different communities. This paper analyzes the performance of orthogonal matching pursuit (OMP) algorithm in recovering magnitude decaying sparse signal in compressive sensing. A concept of Peak Signal Interference Ratio (PSIR) is defined which relates to the identification of atoms in OMP algorithm. Moreover, the relationship between PSIR and the magnitude decaying rate is given and analyzed, which bridges the gap between the performance of OMP and the signal magnitude property. The aforementioned result can be verified through experimental simulation of recovering Zero-one sparse signal and different magnitude decaying sparse signals.